A critical survey of twisted spectral triples beyond the Standard Model

We review the applications of twisted spectral triples to the Standard Model. The initial motivation was to generate a scalar field, required to stabilise the electroweak vacuum and fit the Higgs mass, while respecting the first-order condition. Ultimately, it turns out that the truest interest of the twist lies in a new—and unexpected—field of 1-forms, which is related to the transition from Euclidean to Lorentzian signature.